Resource network with limited capacity of attractor vertices

An asymmetric regular resource network with limited capacity of attractor vertices is considered. Provided attractors’ capacity is unlimited they accumulate all the resource of a network, except some small volumes left in the rest vertices. On the other hand, attractors of limited capacity are saturated, and then another set of vertices starts attracting the rest resource. We refer to this phenomenon as to secondary attractivity, and such vertices, respectively, are called secondary attractors. We study the flows in a network with different total amount resource and search the threshold values which lead to a new behavior of a network.